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Temperature game

Harry is dissatisfied with both Celsius and Fahrenheit Scale and wanted to design his own temperature scale based on ethyl alcohol.
On the Celsius scale ethyl alcohol has melting point \(-117^\circ C\) and boiling point \(78 ^\circ C\) but on his new scale calibrated in degree \(E\). he finds melting point \(0^\circ E\) and boiling point \(200^\circ E\).

What is the temperature corresponding to the melting point of water on this scale?

Imaginary bonus for finding the boiling point of water and deriving the formula.

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